Type IV codes over a non-local non-unital ring
Adel N. Alahmadi, Amani Alkathiry, Alaa Altassan, Widyan Basaffar, Alexis Bonnecaze, Hatoon Shoaib, Patrick Solé · Proyecciones (Antofagasta) · 2020
There is a local ring H of order 4, without identity for the multiplication, defined by generators and relations as H =〈a, b | 2a = 2b = 0, a2 = 0, b2 = b, ab = ba = 0〉. We classify self orthogonal codes of length n and size 2n (called here quasi self-dual codes or QSD) up to the length n = 6. In particular, we classify quasi Type IV codes (a subclass of Type IV codes, viz QSD codes with even weights) up to n = 6.